For questions about geometric shapes, congruences, similarities, transformations, as well as the properties of classes of figures, points, lines, angles.

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votes
1answer
19 views

Calculating degree of abduction from pitch reading

I'm trying to determine the abduction of a person's arm from a wearable pitch sensor, so the minimum pitch reading when the arm is relaxed at the person's side, outputs a value of ...
0
votes
0answers
15 views

Show: $s_A\circ s=s\circ s_B \iff$ $d$ is the bisector of $[AB]$

Consider two distinct points $A$ and $B$ of the plane space. Let $d$ be a line different from $(AB)$. Denote $s_A$ (resp. $s_B$) the central symmetry of center $A$ (resp. $B$). Denote $s$ the symmetry ...
2
votes
1answer
31 views

Is it possible to solve the following problem without any coordinate system and if so, how?

Let $ABC$ be a triangle ($A \notin (BC)$) in the plane space. Let $x,y$ and $z$ be three reals and let $M, P$ and $S$ be the points defined by: $$\vec{AM}=x\vec{AB},\quad \vec{AP}=y\vec{AC},\quad ...
-4
votes
2answers
38 views

Existence of a Triangle with a Multiplicity

A finite set $S$ of unit squares is chosen out of a large grid of unit squares. The squares of $S$ are tiled with isosceles right triangles of hypotenuse $2$ so that the triangles do not overlap each ...
0
votes
2answers
28 views

Find equation of a plane throw two given point and orthogonal to another space

I have $\pi:4y-3z-4=0 \quad A=(2,4,4) \quad B=(2,-2,-4)$. I have to calculate the equation of the plane $\sigma$ throw $A$ and $B$ and orthogonal to $\pi$. What is the solution? Thanks in advice!
0
votes
0answers
25 views

Answer Verification for Circle Problem

Nine distinct positive integers are arranged in a circle, in a way that the product of any two non-adjacent numbers in the circle is a multiple of $n$ and the product of any two adjacent numbers in ...
1
vote
1answer
12 views

A finite group of isometries is isomorphic to a subgroup of $SO(3)$?

I want to show that the rotation group of a polyhedron is isomorphic to a finite subgroup of $SO(3)$, since then I can use the classification of those subgroups to classify all polyhedral rotation ...
1
vote
3answers
38 views

Proving that $BI$, $AE$ and $CF$ are concurrent?

Let $ABC$ be a triangle, and $BD$ be the angle bisector of $\angle B$. Let $DF$ and $DE$ be altitudes of $\triangle ADB$ and $\triangle CDB$ respectively, and $BI$ is an altitude of $\triangle ...
2
votes
2answers
40 views

What is the equation for this wave?

So it would be hard to describe it, it's better to see it yourself: http://physics.info/waves/surface-wave.html (Angular velocity of rotating points is constant I presume) What is it called? What ...
2
votes
0answers
31 views

Are the 14 Bravais lattices really distinct?

I have learned that there are 14 distinct Bravais lattices in 3D and any other thought lattice form could be reduced to or expressed in one of these 14 forms. But the primitive unit cell for f.c.c ...
3
votes
1answer
41 views

Geometrical or Physical significance (interpretation) of the inner-product $\langle A,B \rangle := Trace (AB^t)$ over $M_n(\mathbb R)$

$\langle A,B \rangle := Trace (AB^t)$ is an inner product over the vector space $M_n(\mathbb R)$ of all real matrices of size $n$ , I would like to know whether this inner-product has any Geometrical ...
0
votes
1answer
36 views

Connected components of Lorentz Group $O_1(3)$

Let us consider the set of all vector isometries of the space $\mathbb{E}^3_1$, $O(1,3)$. I know this group has four connected components but I can't prove it. Could someone help me? I'm completely ...
5
votes
1answer
101 views

Inequalites of triangle side with $abc = 1$

Let $a,b,c$ be the sides of a triangle with $abc=1$. Prove that $$ \frac{\sqrt{b+c−a}}{a} + \frac{\sqrt{c+a-b}}{b} + \frac{\sqrt{a+b−c}}{c} \ge a+b+c $$
0
votes
1answer
30 views

How prove that $AB>AC$ in triangle $ABC$?

Point $D$ is chosen inside $\triangle ABC$, and point $E$ on segment $BD$ such that $BD=CE$. Suppose $\angle ABD=\angle ECD=10^{\circ}$, $\angle BAD=40^{\circ}$, and $\angle CED=60^{\circ}$.How prove ...
1
vote
1answer
51 views

Proving $B$, $C$, $D'$ and $E'$ to be concyclic iff $AB+AC=3BC$?

Let $ABC$ be a triangle with incenter $I$. The incircle of $ABC$ touches $AC$ at $D$ and $AB$ at $E$. Let $DD'$ and $EE'$ be the diameters of the incircle. Prove that $B$, $C$, $D'$ and $E'$ are ...
1
vote
2answers
35 views

about shortest path between points

Let $P=(0,1)$ and $Q=(4,1)$ be points on the plane. let $A$ be a point which moves on the $x$-axis between the point $(0,0)$ and $(4,0)$. let $B$ be a point which moves on the line $y=2$ between the ...
2
votes
2answers
48 views

Labelling the Vertices of Dodecahedron

Dodecahedron has 20 vertices. I want to label them by $1,2,3,4,5$ with the following rule. The five vertices of each face should have different labels. Q. What ...
1
vote
2answers
22 views

how to find spherical coordinates of adjacent vertices surrounding central vertex in A3/D3 lattice

How could you define (using spherical coordinate system) all the adjacent vertices directly connected to a central vertex in a tetrahedral octahedral honeycomb? Alternatively it would be useful to get ...
0
votes
0answers
38 views

Triangle $ABC$ and equilateral triangles $ABC'$, $BCA'$ and $ACB'$.

We consider a triangle $ABC$ whose angles are less then $120°$ and construct the equilateral triangles $ABC'$, $BCA'$ and $ACB'$, exterior to $ABC$. $I$ denotes the intersection of $(AA')$ and ...
0
votes
0answers
19 views

Study the caracteristics of the transformation $f=r\circ t \circ h$.

Let $OABC$ be a square with $(\vec{OA},\vec{OC})=\frac{\pi}{2}$. Let $r$ be the rotation of center $B$ and angle $\alpha=\frac{\pi}{2}$, $t$ the translation of vector $\vec{CA}$, $h$ the homothetic ...
2
votes
3answers
47 views

Given an equilateral triangle, show that $MA + MC = MB$.

I have to solve the following problem: Consider an equilateral triangle $ABC$ and $\mathcal{C}$ its circumscribed circle. Let $M$ be a point located on the arc of the circle defined by $[AC]$ which ...
0
votes
1answer
21 views

Geometry parallel angles

1 picture. Find value of u, v and w 2nd picture. find value of x
-1
votes
1answer
32 views

Angles and Parallel

a and e are both (...), both have arms to the right on n g and b are both (...), both have arms to the left on n I'm not getting this, I am taught in another language so I do not know what it's ...
0
votes
0answers
8 views

Is this a Hamiltonian Directed Cycle? Need help proving.

Say that there is $S$, a finite set of unit squares. So, $S$ is chosen from a larger grid of unit squares. The unit squares of $S$ are tiled with isoceles right triangles. Each of these triangles has ...
0
votes
1answer
27 views

Proving that the dot product is distributive?

I know that one can prove that the dot product, as defined "algebraically", is distributive. However, to show the algebraic formula for the dot product, one needs to use the distributive property in ...
2
votes
1answer
24 views

Similarity of triangles?

The question is: "$ABCD$ is a quadrilateral in which angle $B =$ angle $C$ and $AC$ bisects angle $BAD$. If $BA$ and $CD$, when extended, meet at $E$, prove that $AD/DC = AE/BE$." I'm finding this ...
1
vote
1answer
17 views

Determining direction from three points on a line

I have a small geometry problem that for some reason I just can't get a grasp on. You're given three points on a line in 3D space, p1, p2, p3. (assume for simplicity that they're named ...
0
votes
2answers
43 views

If ABCD is a square and M is any point on CD…

If $ABCD$ is a square and $M$ is any point on $CD$, the angle bisector of angle $BAM$ intersects $BC$ at $K$ then how to prove that $MA=DM + BK$.
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votes
1answer
25 views

Getting angle vector makes with the x-axis

If we have the velocity of a particle moving on a path, $\frac{dy}{dx}=0.43$ then why can we say that the angle the velocity vector makes with the x axis is $\arctan(0.43)$? I don't understand why ...
2
votes
2answers
78 views

$\sin \left( {5x} \right) = 2\sin \left( {3x} \right)\sin \left( {4x} \right)$

ask gentlemen to help solve the equation Where the real number $$ x \in \mathbb{R}: \sin \left( {5x} \right) = 2\sin \left( {3x} \right)\sin \left( {4x} \right); $$ I notice that $$x = k\pi \quad ...
1
vote
1answer
14 views

The ratio of the perimeter of rect P to the perimeter of rect Q is 2:5. The area of rectangle P is 12 sq ft. What is the area of rect Q? [closed]

The ratio of the perimeter of rectangle P to the perimeter of rectangle Q is 2:5. The area of rectangle P is 12 square feet. What is the area of rectangle Q?
1
vote
0answers
23 views

Two similar regular polyhedra have given surface areas. What is the ratio of their edge lengths? [closed]

Two similar regular polyhedra have surface areas 16 cm.sq. and 64 cm.sq. What is the ratio of their edge lengths?
1
vote
0answers
20 views

Twisted colouring problem

I had doubts in the following similar looking questions I came across:- $Q1.$ The Cartesian plane is coloured with 2 colours. Prove that there exists 3 points of the same colour, which are the ...
1
vote
1answer
13 views

Given Lines t, m, and n are tangent to the circle at W, Y, and X (respectively). What is the arc of WY [closed]

The tangent lines t and m meet outside the circle at point C, lines m and n meet at point B and t and n meet at point A. Angle XBY is 50 degrees, Angle WAX is 60 degrees. I need to find the arc of ...
0
votes
1answer
42 views

Parametrisation of curves in 3D and using properties of $\mathbf{r}(t)$ to show that the curve is on the surface of a sphere.

A curve $C$ in $\mathbb R^3$ has a parametrisation $\mathbf r(t)$. Suppose $\mathbf r(t)\neq 0 \,\forall t\in \mathbb R$ and $\mathbf r(t)\cdot\mathbf r'(t)=0$ for all points of $C$. Show that $C$ ...
0
votes
2answers
38 views

$ABCD$, $P$ is any interior point, $PA=24, PB=32, PC=28, PD=45$

could anyone tell me how to solve it? I have a convex quadrilateral $ABCD$, $P$ is any interior point, $PA=24, PB=32, PC=28, PD=45$ cm, I need to know the perimeter of $ABCD$. Thanks for helping. ...
0
votes
0answers
30 views

Show that circle generates the surface $(x^2+y^2+z^2)(\frac{x^2}{a^2}+\frac{y^2}{b^2})=x^2+y^2$

$POP'$ is a variable diameter and the ellipse $z=0, \frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and a circle is described in the plane $PP'ZZ'$ on $PP'$ as diameter. Prove that as $PP'$ varies, the circle ...
0
votes
2answers
13 views

Using Similar Triangles to solve for the equation of a line

Consider points A=(−10,−4) and C=(8,5). The point B is on the line passing through A and C. The x-coordinate of B is −1. Determine the y-coordinate of the point B. This question has been asked ...
0
votes
0answers
22 views

Are isosceles right triangles the only ones whose circumcenters lie on their incircles? [duplicate]

I recently (stupidly) asked this question, to which user Blue responded quickly with the example of the isosceles right triangle. Which triangles have circumcenters on their incenters? Do they have to ...
0
votes
1answer
47 views

Is there any triangle whose circumcenter lies on its incircle?

Is it possible for a triangle's circumcenter to lie on its incircle? My guess is yes, but I haven't succeeding in explicitly finding one or proving that it exists.
1
vote
1answer
51 views

Prove that four points lie on a circle.

Let $ABC$ be a triangle such that $2AB=AC+BC$. Show that the incentre, the circumcircle, midpoint of $AC$ and midpoint of $BC$ lie on a circle. I reduced the question to prove that both midpoints, ...
3
votes
1answer
53 views

If the red curve is an ellipse, is the green curve also an ellipse? [duplicate]

See the figure below: The red curve is an ellipse; the blue curve is a unit circle. Green curve is the locus of the circle center. Is the green curve an ellipse?
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votes
2answers
41 views

Quadratic Forms in $n$ dimensions

In my linear algebra high school textbook, there is a 'Project' that extends geometrical ideas to '$n$-dimensional space'. I have no idea what to do or where to begin for this question. Show ...
0
votes
2answers
15 views

Given a line, calculate a perpendicular line to make a T shape

I am working with SVG vector graphics, and I want to make a dynamic T shape by adding a perpendicular line. I have a line with two points (4,17) and (11,3). How can I figure out (x1,y1) and (x2,y2)? ...
0
votes
2answers
46 views

About the sum of sines of two angles

Suppose that $0\le \alpha\le \pi/2$ and $0\le \beta\le \pi/2$ such that $\alpha+\beta\ge \pi/2$. Can we prove that $\sin(\alpha)+\sin(\beta)\ge 1$?
0
votes
1answer
23 views

Find ray between an angle in the same plane as the angle

If I have an angle $\angle{ABC}$, I want to know how to find a ray $\overrightarrow{BD}$ such that $\overrightarrow{BD}$ is in the same plane as $\angle{ABC}$, and the measure of $\angle{ABD}$ is some ...
0
votes
1answer
16 views

Distance of a point from a line specified by coordinates

I'm working on an open source program that involves drawing and it would be helpful to see which line is closest to the user's selection. I have a point specified by coordinates and a line specified ...
1
vote
0answers
42 views

Quadric and tangents planes

Let $Q$ be the quadratic $x^2 + 4xy - 2y^2 + 6z^2 + 2y +2z = 0$ Prove that $Q$ is a cone and find its vertex. Write the tangent plane $A$ to the cone in $(0,0,0)$ and say which kind of conic is the ...
0
votes
1answer
42 views

Weird vector projection form

Let $C^0[1,3]$ be the $\Bbb R$-vector space equipped with the usual scalar product (by the integral ). Calculate the projection of the function $f(x)= 1/x$ onto the subspace $W = L\{x\}$ Well, my ...
2
votes
3answers
52 views

Lazy Caterer's Problem: why a new line can cut all the others

The lazy caterer's problem is to figure out the maximum number of pieces formed by $n$ straight cuts of a pizza. Any time two cuts meet new pieces are generated, so for maximum number of pieces it ...